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Combining effects: sum and tensor
"... We seek a unified account of modularity for computational effects. We begin by reformulating Moggi’s monadic paradigm for modelling computational effects using the notion of enriched Lawvere theory, together with its relationship with strong monads; this emphasises the importance of the operations ..."
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Cited by 29 (4 self)
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We seek a unified account of modularity for computational effects. We begin by reformulating Moggi’s monadic paradigm for modelling computational effects using the notion of enriched Lawvere theory, together with its relationship with strong monads; this emphasises the importance of the operations that produce the effects. Effects qua theories are then combined by appropriate bifunctors on the category of theories. We give a theory for the sum of computational effects, which in particular yields Moggi’s exceptions monad transformer and an interactive input/output monad transformer. We further give a theory of the commutative combination of effects, their tensor, which yields Moggi’s sideeffects monad transformer. Finally we give a theory of operation transformers, for redefining operations when adding new effects; we derive explicit forms for the operation transformers associated to the above monad transformers.
Generic trace semantics via coinduction
 Logical Methods in Comp. Sci
, 2007
"... Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace ..."
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Cited by 17 (6 self)
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Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace
Probability and Nondeterminism in Operational Models of Concurrency
 In Proc. CONCUR, LNCS
, 2006
"... Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analy ..."
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Cited by 12 (1 self)
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Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analysis of randomized distributed algorithms. 1
Reasoning about probabilistic sequential programs ∗
"... A complete and decidable Hoarestyle calculus for iterationfree probabilistic sequential programs is presented using a state logic with truthfunctional propositional (not arithmetical) connectives. 1 ..."
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Cited by 12 (11 self)
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A complete and decidable Hoarestyle calculus for iterationfree probabilistic sequential programs is presented using a state logic with truthfunctional propositional (not arithmetical) connectives. 1
Trueconcurrency probabilistic models Branching cells and distributed probabilities for event structures
, 2006
"... ..."
Continuous Previsions ⋆
"... Abstract. We define strong monads of continuous (lower, upper) previsions, and of forks, modeling both probabilistic and nondeterministic choice. This is an elegant alternative to recent proposals by Mislove, Tix, Keimel, and Plotkin. We show that our monads are sound and complete, in the sense tha ..."
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Cited by 6 (4 self)
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Abstract. We define strong monads of continuous (lower, upper) previsions, and of forks, modeling both probabilistic and nondeterministic choice. This is an elegant alternative to recent proposals by Mislove, Tix, Keimel, and Plotkin. We show that our monads are sound and complete, in the sense that they model exactly the interaction between probabilistic and (demonic, angelic, chaotic) choice. 1
Probabilistic trueconcurrency models: branching cells and distributed probabilities, in "Information and Computation
, 2006
"... This paper is devoted to trueconcurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finit ..."
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Cited by 5 (1 self)
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This paper is devoted to trueconcurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finite. Locally finite event structures exhibit “finite confusion”; in particular, under some mild condition, confusionfree event structures are locally finite. In locally finite event structures, maximal configurations can be tiled with branching cells: branching cells are minimal and finite substructures capturing the choices performed while scanning a maximal configuration. A probabilistic event structure (p.e.s.) is a pair (E, P), where E is a prime event structure and P is a probability on the space of maximal configurations of E. We introduce the new class of distributed probabilities for p.e.s.: distributed probabilities are such that random choices in
A Local Algorithm for Checking Probabilistic Bisimilarity
"... Abstract—Bisimilarity is one of the most important relations for comparing the behaviour of formal systems in concurrency theory. Decision algorithms for bisimilarity in finite state systems are usually classified into two kinds: global algorithms are generally efficient but require to generate the ..."
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Cited by 1 (1 self)
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Abstract—Bisimilarity is one of the most important relations for comparing the behaviour of formal systems in concurrency theory. Decision algorithms for bisimilarity in finite state systems are usually classified into two kinds: global algorithms are generally efficient but require to generate the whole state spaces in advance, and local algorithms combine the verification of a system’s behaviour with the generation of the system’s state space, which is often more effective to determine that one system fails to be related to another. Although local algorithms are well established in the classical concurrency theory, the study of local algorithms in probabilistic concurrency theory is not mature. In this paper we propose a polynomial time local algorithm for checking probabilistic bisimilarity. With mild modification, the algorithm can be easily adapted to decide probabilistic similarity with the same time complexity. Keywordsconcurrency; probabilistic bisimilarity; local algorithm; probabilistic labelled transition systems; I.
Deriving Predicate Transformer Semantics for pGCL from its Direct Semantics
"... In [McM] McIver and Morgan have introduced pGCL, an imperative programming language with guarded command incorporating both erratic and probabilistic nondeterminism. For verifying pGCL programs they associate with every pGCL program P a predicate transformer wp(P) : E(S) → E(S) where S is a countab ..."
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In [McM] McIver and Morgan have introduced pGCL, an imperative programming language with guarded command incorporating both erratic and probabilistic nondeterminism. For verifying pGCL programs they associate with every pGCL program P a predicate transformer wp(P) : E(S) → E(S) where S is a countable set of states and E(S) = [0, 1] S ordered pointwise. We show how to derive McIver and Morgan’s predicate transformer semantics from a more intuitive direct semantics associating with every progrem P a function [[P]] : S → PU (V(S)) where PU is the upper (or Smyth) powerdomain and V(S) the probabilistic powerdomain of S ⊥ which for convenience can be identified with the set of function µ: S → [0, 1] with ∑ s∈S µ(s) ≤ 1 (of course, for A ⊆ S we define µ(A) as ∑ s∈A µ(s)). Following a suggestion in [TKP] we define for f: S → PU (V(S) its associated
CEA LIST
"... Abstract. Having a precise yet sound abstraction of the inputs of numerical programs is important to analyze their behavior. For many programs, these inputs are probabilistic, but the actual distribution used is only partially known. We present a static analysis framework for reasoning about program ..."
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Abstract. Having a precise yet sound abstraction of the inputs of numerical programs is important to analyze their behavior. For many programs, these inputs are probabilistic, but the actual distribution used is only partially known. We present a static analysis framework for reasoning about programs with inputs given as imprecise probabilities: we semantics based on an extension of DempsterShafer structures. We prove the correctness of our approach and show on some realistic examples the kind of invariants we are able to infer. 1